6.5 Average Value of a Function/1

Find the average value of the function on the given interval.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(x) = 4x-x^2, \quad (0, 4) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} f_{avg} &= \frac{1}{4-0} \int_{0}^{4} (4x-x^2) dx \\[2ex] &= \frac{1}{4} \int_{0}^{4} (4x-x^2) dx \\[2ex] &= \frac{1}{4} \left[\bigg( 4x-\frac{x^3}{3}\bigg) \right]_0^4 \\[2ex] &= \frac{1}{4} \bigg(8-\frac{8}{3}\bigg)-\bigg(-8+\frac{8}{3}\bigg) \\[2ex] &= \frac{1}{4} \left[\bigg( \frac{32}{4}\bigg) \right] \\[2ex] &= \frac{8}{3} \end{align} }